How to work with layers in 2.9x like in previous versions (2.7x)
The 2.7 Layers have been replaced by Collections, you should now use Collections. Basically one former Layer is now one Collection (and when you open an old Blender file Layers are automatically replaced by Collections).

You're confusing Layers with View Layers, which are completely different things, View Layers are useful for the Compositor (which is not the case in this tutorial).
With View Layers you're just changing the visibility settings of the current scene for later compositing purpose, so when you modify an object, it's the exact same object as the one of another View Layer.